### Abstract

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t_{att}) and detachment (t_{det}), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k _{stiff}) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F_{hs}(t)) to sinusoidal length perturbations (L _{hs}(t)) was predicted by the analytical expression in the frequency domain, (F̃_{hs}(ω)/L̃_{hs}(ω)) = (t̄_{att}/t̄_{cycle})Nk̄_{stiff}(iω /(t̄_{att}^{-1} + iω)); where t̄_{att} = mean value of t_{att}, t̄_{cycle} = mean value of t _{att} + t_{det}, k̄_{stiff} = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (L_{hs}) was furthermore predicted by the analytical expression in the time domain, F_{hs}(t) = (t̄_{att}/ t̄_{cycle})Nk̄_{stiff}L_{hs} e ^{-t/t̄att}. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄_{att}^{-1}. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.

Original language | English (US) |
---|---|

Pages (from-to) | 760-769 |

Number of pages | 10 |

Journal | Biophysical Journal |

Volume | 93 |

Issue number | 3 |

DOIs | |

State | Published - Aug 2007 |

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### ASJC Scopus subject areas

- Biophysics

### Cite this

*Biophysical Journal*,

*93*(3), 760-769. https://doi.org/10.1529/biophysj.106.101626

**Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis.** / Palmer, Bradley M.; Suzuki, Takeki; Wang, Yuan; Barnes, William D.; Miller, Mark S.; Maughan, David W.

Research output: Contribution to journal › Article

*Biophysical Journal*, vol. 93, no. 3, pp. 760-769. https://doi.org/10.1529/biophysj.106.101626

}

TY - JOUR

T1 - Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

AU - Palmer, Bradley M.

AU - Suzuki, Takeki

AU - Wang, Yuan

AU - Barnes, William D.

AU - Miller, Mark S.

AU - Maughan, David W.

PY - 2007/8

Y1 - 2007/8

N2 - The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (Fhs(t)) to sinusoidal length perturbations (L hs(t)) was predicted by the analytical expression in the frequency domain, (F̃hs(ω)/L̃hs(ω)) = (t̄att/t̄cycle)Nk̄stiff(iω /(t̄att-1 + iω)); where t̄att = mean value of tatt, t̄cycle = mean value of t att + tdet, k̄stiff = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (Lhs) was furthermore predicted by the analytical expression in the time domain, Fhs(t) = (t̄att/ t̄cycle)Nk̄stiffLhs e -t/t̄att. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄att-1. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.

AB - The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (tatt) and detachment (tdet), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k stiff) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (Fhs(t)) to sinusoidal length perturbations (L hs(t)) was predicted by the analytical expression in the frequency domain, (F̃hs(ω)/L̃hs(ω)) = (t̄att/t̄cycle)Nk̄stiff(iω /(t̄att-1 + iω)); where t̄att = mean value of tatt, t̄cycle = mean value of t att + tdet, k̄stiff = mean stiffness, and ω = 2π x frequency of perturbation. The simulated force response due to a length step (Lhs) was furthermore predicted by the analytical expression in the time domain, Fhs(t) = (t̄att/ t̄cycle)Nk̄stiffLhs e -t/t̄att. The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2πc, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t̄att-1. Experimental results from activated cardiac muscle examined at different temperatures and containing predominately α- or β-myosin heavy chain isoforms were found to be consistent with the above interpretation.

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UR - http://www.scopus.com/inward/citedby.url?scp=34547650842&partnerID=8YFLogxK

U2 - 10.1529/biophysj.106.101626

DO - 10.1529/biophysj.106.101626

M3 - Article

C2 - 17496022

AN - SCOPUS:34547650842

VL - 93

SP - 760

EP - 769

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 3

ER -